It is a parabolic partial differential equation involving the option price \(V,\) the price of the underlying stock \(S,\) the volatility \(\sigma,\) and the risk free rate \(r.\) As it is simple to account for annualized dividend payments \(d\), these are included in the code, too.

Implementation

Finite differences discretization of the spatial derivative operators

Runge-Kutta schemes for the integration in time (currently first to 4th order low-storage schemes)

Currently only simple Dirichlet type boundary conditions are implemented